The metric \(\eta ^{(j)}\) , for \(j=2,1,0\) , is called a \(j\) -metric. It is important to mention that every proper groupoid can be endowed with a 2-metric (more generally, an \(n\) -metric as defined below) and if a Lie groupoid admits a 2-metric then it is weakly linearizable. For more details visit [1]}, [2]}.
